Nicklaus won the event three times, the others twice.
Day, the 2016 champion, stayed in the hunt with a tidy four-under-par 68 at TPC Sawgrass in Ponte Vedra Beach, Florida.
He will start the final round in fourth place, three behind Spanish leader Jon Rahm and two back of Rory McIlroy and Tommy Fleetwood.
Day was slammed last Thursday when he pulled out of the Arnold Palmer Invitational after seven holes, later disclosing that an MRI scan earlier in the week had revealed a tear in a disc in his back.
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That did not sit well with some fans who had bet on him to win and who were upset he had not disclosed the injury before the tournament.
There was further criticism when Day was subsequently photographed standing in line with his family at Disney World, even though bed rest is often the last thing back specialists recommend for their patients.
Day shrugged off the criticism, revealing that after his withdrawal he had undergone four spinal injections in an effort to alleviate the pain.
Day, whose back issues date back nearly two decades, was pleasantly surprised by his lofty position through 54 holes.
"I was just trying to get upright and be able to swing (a week ago)," the former world number one said.
"So it's actually quite nice to have the opportunity to be in contention tomorrow. I'm very blessed about that.
"If I can walk away hopefully a champion tomorrow, then that's a good little comeback, especially with how I was feeling last week."
(Reporting by Andrew Both in Cary, North Carolina, editing by Nick Mulvenney)
